Answered: 6. Prove that if A, B E Mnxn (F) are…

6. Prove that if A, B E Mnxn (F) are similar, then tr(A) = tr(B) (where tr(M) is the trace of the matrix M). (Remember that class notes and/or the text can help!)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.6: Rank Of A Matrix And Systems Of Linear Equations

Problem 64E

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Question

6. Prove that if A, B = Mnxn (F) are similar, then tr(A) = tr(B) (where tr(M) is the trace of
the matrix M). (Remember that class notes and/or the text can help!)

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Step 1: A,B belongs to M

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Step 2: Tr(A=Tr(B)

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